Yeah, you'll probably never find her name. Most shows only put a short list of credits at the ends of episodes. You could try looking there anyway, though. You might get lucky. Look through credits of those episodes where you've seen her, look up the names listed, see if anything matches, etc.
You can post screencaps of credits here, if you don't read Korean. I can try to help, but if she just has a line in a single episode or something, they're not likely to put her in the credits.